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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_3592_Библиотеки_им_академика_М_И_Перельмана
.pdf
Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
https://t.me/medicina_free
Step 4. Now, we choose the number of principal components (n) using the
condition:
⎛
⎜
⎜
⎝
∑
=
jn1
∑
⎞
λ
j
⎟
⩾
m
=
i
1
X, (14.1)
⎟
λ
i
⎠
where X is the cut-off, varying from 0.90 to 0.99 with a step size of 0.01,
and m represents the total number of eigenvalues.
Step 5. Now, we compute the contribution to the feature extraction result of
each feature component as follows:
=∣∣
CV,
∑
iki
=
kn1
(14.2)
where
∣∣V
ki
Step 6. Finally, we sort the
indicates the ith entry of
V
ki
shows the absolute value of
in descending order and select the first n features
C
i
, i = 1, 2, …, m and k = 1, 2, …, n.
V
k
.
V
ki
components which will give the reduced number of dominant features
without losing the feature values.
14.3.5 Support vector machine
For training the machine learning classifier to perform tissue classification, we have
used a classifier based on SVM [16, 17]. SVM is a supervised learning model which
performs classification by constructing a hyper-plane between the data points. This
hyper-plane optimally separates the data into the desired number of classes [47]. The
points near the hyper-plane are called support vectors and their distance from the
hyper-plane is called the margin. The marginal hyper-planes are the two hyperplanes which are constructed on each side of the hyper-plane and the objective is to
maximize the distance of the data points from these marginal hyper-planes [42, 43].
For performing the non-linear classification, kernel functions are used [44, 45].
Commonly used kernel functions are linear, the radial basis function (RBF) and
polynomial (of different orders) [46]. The mathematical description of SVM is given
below.
Let us consider a two-class classification task with the training sample of patterns
( , ), 1, 2, , }
ii
є− +
{1, 1}
i
=…mn i l
represents the corresponding target values,
, where
q
represents input data for ith sample and
єmR
i
is the total number of
training samples and q is the dimension of the input space. The SVM model can be
represented in feature space by the following equation:
where
represents the kernel function which maps the input vector into higher
Φ m()
dimensional space,
hyper-plane and T denotes transpose. The decision rule is mathematically represented by the following equation:
T
ωα=Φ +px m() ( ) ,
(14.3)
represents bias,ωis a weight vector which is normal to the
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Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
https://t.me/medicina_free
T
ωα
Φ + ⩾+ =+
mn
() 1 if 1
ii
T
ωα
Φ + ⩽− =−
mn
() 1 if 1.
i
i
(14.4)
The non-linear kernel function finds the separating hyper-plane with a maximum
margin
2
between the classes in a feature space. To find the optimal separating
ω∥∥
hyper-plane, equation (14.3) is minimized as shown by the following equation:
1
2
,
€
∑
i
=
il1
ωξ+
2
(14.5)
where€is the trade-off parameter between the error and margin, andξis a slack
variable. By using Lagrangian multipliers (£) in dual form, the equation (14.3) can
be transformed into the following optimization problem:
maximize
l
−
£ ££nnK m m
∑∑∑
iijijfij
===
i
111
1
2
ilj
l
(, )
(14.6)
subject to
=⩾∀
£n £ i0, 0
∑
ii i
=
il1
(14.7)
where
fi j i
=Φ ·ΦKm m m m( , ) ( ) ( ). (14.8)
T
j
Finally, the final decision function is mathematically represented by the following
equation:
px £nK m m() ( , ) .
∑
ii f i j
=
il1
α=+
(14.9)
14.3.6 Machine learning (ML) paradigm for class prediction
Figure 14.4 shows the block diagram of the ML system used in this study using the
fusion of plaque texture-based and wall-based measurement features (as shown by the
arrows on the left and right). The patient population is divided into two components:
the training population and the testing population. The training population is used for
computing the learning parameters during the ML process. These parameters are
computed using the training grayscale coronary wall region and corresponding carotid
gold standard risk labels. This gold standard is derived from the concept of the second
hypothesis, which states that atherosclerotic plaque has a common genetic make-up, as
discussed before in step 1 [16, 17]. In the ML paradigm, one computes the offline
grayscale plaque features and trains these features according to the gold standard risk
labels derived from the carotid artery plaque burden. These offline parameters are then
transformed by the online grayscale wall features computed from the test images to
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Texture
Features
Wall Measurement
Features
Carotid Plaque
Burden
Kernel Type
High/Low
Grayscale Ring
Images (Training)
Feature Extraction Feature Extraction
Extracted Offline
Features
Offline SVM
Classification
Machine Learning
Parameter
Training-Phase Testing-Phase
High/Low
Grayscale Ring
Images (Testing)
Extracted Online
Features
Online SVM
Classification
Low Risk
Predicted Class
Performance Evaluation of system
Stability Reliability
Texture Features
Wall Measurement
Features
High Risk
Predicted Class
Figure 14.4. Improved coronary risk assessment system (cRAS) using the ML paradigm utilizing PCA with
the fusion of plaque texture-based and wall-based measurement features. Gray boxes show novel wall-based
measurement features.
predict its risk label. Finally, the process of ML is repeated for the cyclic combinations
as per the K-fold combinations. Since there are ten parts (K10 protocol: 90% training
and 10% testing), we therefore rotate this combination ten times to ensure that each set
of 10% testing data gets a chance to become a training dataset. Each combination yields
the stratification accuracy using the ML system. The mean value of the classification
accuracy is then computed, which determines the final accuracy of the ML system.
Furthermore, to separate the features in the SVM framework, we have adopted both a
linear and four non-linear kernel functions [17], namely the RBF, and polynomial
functions of order 1, 2 and 3. These kernel functions are used by the SVM during its
training and testing phases.
14.4 Results
The main observations here are to see the effect of fusion of wall-based measurement
features with plaque texture-based features on the stratification accuracy in the ML
framework. These results will characterize (i) the PCA polling process, the best
kernel design during the classification process and (iii) cut-off values between
memorization versus generalization for a dataset size.
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); 55—complexity;
3
Table 14.9. Dominant features selected at each PCA-based cut-off using (a) stand-alone plaque texture-based features and (b) plaque texture-based features fused with
wall-based measurement features.
(a) Using stand-alone plaque texture-based features
Cut-offs F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F15 F16
); 43—busyness; 44—complexity; 52—I7; 54—contrast (C
0
); 42—contrast (C
1
(b) Using plaque texture-based features fused with wall-based measurement features
The numerical numbers listed in the columns have unique feature names and these are as follows: 4—cluster prominence; 6—dissimilarity; 15—difference variance;
16—difference entropy; 21—gray-level non-uniformity; 24—low gray-level run emphasis; 26—short run low gray-level emphasis; 28—long run low gray-level
0.90 52 56 16 15 6
0.91 52 56 16 15 6
0.92 52 56 16 15 6
0.93 52 56 55 26 24 4
0.94 52 56 55 26 24 4
0.95 52 56 55 26 24 4 31
0.96 52 56 55 26 24 4 31
0.97 52 44 56 55 26 42 43 4
0.98 52 55 44 4 26 56 43 35 42 37
0.99 55 52 26 56 44 4 43 28 37 42 35 31 24
0.90 52 56 65 28 16
0.91 52 59 61 56 26 55
0.92 52 59 61 56 26 55
0.93 52 65 59 26 61 55 44
0.94 52 65 59 26 61 55 44
0.95 52 65 55 61 44 56 59 26
0.96 65 52 61 55 44 26 56 59 24
0.97 65 61 52 55 44 26 59 4 56 21
0.98 61 44 65 59 55 26 52 4 56 24 21 43
0.99 44 61 65 55 26 59 52 43 4 37 24 21 54 35 28 42
emphasis; 31—variance; 35—skewness; 37—contrast (C
56—roughness; 59—coronary lumen area; 61—coronary calcium area; 65—coronary wall thickness variability, F—feature.
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14.4.1 Dominant feature selection
Thebestdominantfeaturecombination set can increase the accuracy of the SVM
classifier. The objective of this experiment is to find the best matching set of features to
yield the highest accuracy using a PCA-based polling strategy. This is achieved by taking
different cut-offs ranging from 0.90 to 0.99 in increments of 0.01 for a fixed data size.
Table 14.9 shows the dominant features selected for different PCA-based cut-offs
for (a) stand-alone plaque texture-based features and (b) plaque texture-based
features fused with wall-based measurement features. In both cases, we can observe
that the number of dominant features gradually increases with the increase in PCAbased cut-offs. In table 14.9, for the fusion of plaque texture-based and wall-based
measurement features, the coronary calcium area (feature #61), coronary lumen
area (feature #59) and coronary wall thickness variability (feature #65) are selected
as the dominant features for different PCA-based cut-offs. The selection of
dominant features taking different PCA-based cut-offs for both (a) stand-alone
plaque texture-based features and (b) plaque texture-based features fused with wallbased measurement features is shown in figure 14.5.
14.4.2 Selection of the best kernel function
Since the hyper-plane for stratification is governed by the choice of kernel function
used [47], we therefore choose five types of kernels [ 16, 17], such as linear, RBF, and
polynomial of order 1, 2 and 3, respectively, for optimization in both paradigms:
with and without wall-based measurement features.
For this protocol, we have fixed the data size. Using five different kernel
functions, the accuracy of the SVM classifier for both (a) stand-alone plaque
texture-based features and (b) plaque texture-based features fused with wall-based
measurement features are shown in table 14.10. Figure 14.6(a) and (b) show the
Figure 14.5. Numbers of dominant features versus PCA-based cut-offs using (a) stand-alone plaque texturebased features and (b) plaque texture-based features fused with wall-based measurement features.
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Table 14.10. Classification accuracy using SVM with varying kernel function: (a) stand-alone plaque texture-
based features and (b) plaque texture-based features fused with wall-based measurement features.
(a) Using stand-alone plaque texture-based features (in %)
Kernel functions
Cut-offs
0.90 67.14 76.20 67.14 71.87 74.86
0.91 67.14 76.18 67.14 71.89 74.89
0.92 67.15 76.15 67.15 71.91 74.85
0.93 73.02 87.53 73.02 77.37 82.95
0.94 73.06 87.56 73.06 77.39 82.96
0.95 75.48 89.66 75.48 81.30 85.68
0.96 75.48 89.65 75.48 81.32 85.72
0.97 78.47 91.32 78.47 82.88 86.41
0.98 77.91 92.74 77.91 84.20 89.46
0.99 79.80 93.82 79.80 86.63 92.03
Average 73.47 86.08 73.47 78.68 82.98
SD 4.87 7.12 4.87 5.45 6.22
(b) Using plaque texture-based features fused with wall-based measurement features (in %)
0.90 78.24 86.03 78.24 77.66 81.54
0.91 69.63 85.13 69.63 77.61 80.24
0.92 69.64 85.12 69.64 77.54 80.22
0.93 76.55 91.35 76.55 81.40 85.16
0.94 76.53 91.35 76.53 81.44 85.26
0.95 76.73 91.81 76.73 81.96 85.98
0.96 77.79 93.31 77.79 82.83 87.61
0.97 77.58 95.72 77.58 85.68 91.00
0.98 79.86 96.35 79.86 86.97 93.10
0.99 78.94 96.59 78.94 89.41 94.91
Average 76.15 91.28 76.15 82.25 86.50
SD 3.59 4.49 3.59 4.11 5.19
Linear RBF Poly-1 Poly-2 Poly-3
Poly—polynomial.
graphical representation of the accuracy of the SVM classifier for both (a) standalone plaque texture-based features and (b) plaque texture-based features fused with
wall-based measurement features. We observe that for all the kernel functions, the
mean accuracy of all the PCA-based cut-offs using the fusion of plaque texturebased and wall-based measurement features are higher compared to the stand-alone
option where plaque texture-based features are only considered. Among all the
kernel functions, RBF gave the highest accuracy for all the PCA-based cut-offs,
hence is considered as the best among all four kernel functions. This is consistent
with our other studies [16, 17].
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Figure 14.6. cRAS stratification accuracy versus PCA-based cut-offs for five different kernel functions (linear,
RBF, polynomial-1, polynomial-2 and polynomial-3) using (a) stand-alone plaque texture-based features and
(b) plaque texture-based features fused with wall-based measurement features.
14.4.3 Memorization versus generalization
Since the data size can affect the training coefficients, it is important to know when
the generalization is achieved [16, 17]. In our study, we have varied the data size in
ten intervals ranging from 493 to 4930 in the increment of 493 frames. These 493
frames are randomly selected and then added to the corresponding ongoing pool.
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)
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Since our cRAS is highly dependent upon the grayscale morphological characteristics that change from patient-to-patient, and further the calcium deposit varies
along with the wall-based measurements, it is, therefore, imperative to establish the
metrics by which we can evaluate the performance of our cRAS. We therefore
choose the following evaluation parameters: (a) dominant feature retaining power;
(b) receiver operating characteristic curve of the system; (c) reliability index; and (d)
stability, respectively. The whole idea is to understand the absolute and relative
performance along with the variations in changing parameters, which helps to
understand the bounds of operation. For example, reliability reveals how accurate a
system behaves for different databases. The stability of the system is evaluated if the
deviation of the mean accuracy is within the tolerance limit (say 5%). We want to
emphasize that performance evaluation is equally adopted for both (a) stand-alone
plaque texture-based features and (b) plaque texture-based features fused with wallbased measurement features, demonstrating the comparative approach and showing
the effectiveness of the wall-based measurement features in the cRAS.
Table 14.11 and figure 14.7 shows the variation of the SVM accuracy with
varying data size for both (a) stand-alone plaque texture-based features and (b)
plaque texture-based features fused with wall-based measurement features. We
observe that for all the data sizes, the mean accuracy of all the PCA-based cut-offs,
using the fusion of plaque texture-based and w all-based measurement features was
higher compared to a stand-alone plaque texture-based feature paradigm, as now
the dominant features are selected from a wider, diverse and strong pool of
features.
14.5 Performance evaluation
14.5.1 Dominant feature retaining power of the cRAS
The dominant feature retaining power (DFRP) is the ability of the cRAS to retain
the best dominant features responsible for producing a high accuracy for different
PCA-based cut-offs. It is the ratio of similar dominant features between any two cutoffs, say m and n
cut-off m
SDF )
. Using the notation * for the product, we can mathematically
DF
m
compute DFRP in percentage as [17]
For this study, the DFRP taking different PCA-based cut-offs for both (a) standalone plaque texture-based features and (b) plaque texture-based features fused with
wall-based measurement features is shown in table 14.12. The mean DFRP of all the
PCA-based cut-offs, using the fusion of plaque texture-based and wall-based
measurement features, is almost similar (= 89.32%) as compared to stand-alone
plaque texture-based features (= 90.16%).
, and the number of dominant features selected taking the
−
mn
DFRP(%)
⎛
SDF
=*
⎜
⎝
14-21
DF
−
mn
m
⎞
100. (14.10)
⎟
⎠
)
)
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Table 14.11. Average accuracy of each data size using (a) stand-alone plaque texture-based features and (b)
plaque texture-based features fused with wall-based measurement features.
(a) Using stand-alone plaque texture-based features (in %)
Data size
Cut-offs
0.90 100.00 100.00 100.00 100.00 100.00 100.00 71.06 49.90 76.60 76.20
0.91 100.00 100.00 100.00 100.00 100.00 100.00 71.03 50.00 76.56 76.18
0.92 100.00 100.00 100.00 100.00 100.00 100.00 91.37 92.98 90.32 76.15
0.93 100.00 100.00 100.00 100.00 100.00 100.00 91.39 92.98 90.32 87.53
0.94 100.00 100.00 100.00 100.00 100.00 100.00 95.85 95.01 91.71 87.56
0.95 100.00 100.00 100.00 100.00 100.00 100.00 95.85 95.01 91.66 89.66
0.96 100.00 100.00 100.00 100.00 100.00 100.00 98.09 96.88 94.96 89.65
0.97 100.00 100.00 100.00 100.00 100.00 100.00 98.47 97.42 95.52 91.32
0.98 100.00 100.00 100.00 100.00 100.00 100.00 98.47 98.03 96.56 92.74
0.99 100.00 100.00 100.00 100.00 100.00 100.00 99.27 98.17 97.51 93.82
Average 100.00 100.00 100.00 100.00 100.00 100.00 91.08 86.64 90.17 86.08
SD 0.00 0.00 0.00 0.00 0.00 0.00 10.92 19.43 7.60 7.12
(b) Using plaque texture-based features fused with wall-based measurement features (in %)
0.90 100.00 100.00 100.00 100.00 100.00 100.00 90.75 84.82 90.31 86.03
0.91 100.00 100.00 100.00 100.00 100.00 100.00 90.83 84.79 90.35 85.13
0.92 100.00 100.00 100.00 100.00 100.00 100.00 95.68 96.20 93.70 85.12
0.93 100.00 100.00 100.00 100.00 100.00 100.00 96.36 96.21 93.68 91.35
0.94 100.00 100.00 100.00 100.00 100.00 100.00 96.39 97.08 96.00 91.35
0.95 100.00 100.00 100.00 100.00 100.00 100.00 98.60 98.32 95.94 91.81
0.96 100.00 100.00 100.00 100.00 100.00 100.00 99.30 98.38 97.48 93.31
0.97 100.00 100.00 100.00 100.00 100.00 100.00 99.42 99.03 97.97 95.72
0.98 100.00 100.00 100.00 100.00 100.00 100.00 99.44 99.08 98.23 96.35
0.99 100.00 100.00 100.00 100.00 100.00 100.00 99.50 99.07 98.69 96.59
Average 100.00 100.00 100.00 100.00 100.00 100.00 96.63 95.30 95.24 91.28
SD 0.00 0.00 0.00 0.00 0.00 0.00 3.40 5.64 3.12 4.49
493 986 1479 1972 2465 2958 3451 3944 4437 4930
14.5.2 Receiver operating characteristics
The true positive rate (sensitivity) and false positive rate (100-specificity) are mostly
used to measure the diagnostic capability of the analysis. It is a way to identify how
well the classification methods can detect the true calcium. The true positive rate
and false positive rate
TPR
TPR
can be mathematically formulated as
FPR
=
(True positive False negative)
True positive
+
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(14.11)
Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
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Figure 14.7. Average accuracy versus changing data size for K = 10 and T = 20 using (a) stand-alone plaque
texture-based features and (b) plaque texture-based features fused with wall-based measurement features.
FPR
=
(True nagative False positive)
True negative
+
.
(14.12)
True positive/False positive is defined as the number of times a high-risk patient is
correctly/incorrectly identified with respect to the carotid plaque burden (gold
standard) risk labels. Similarly, True negative/False positive is defined as the number
of times a high-risk patient is incorrectly identified.
The receiver operating characteristic can be graphically represented using the true
positive rate and false positive rate and is generally used to quantify the diagnostic
accuracy of the analysis. Using the carotid plaque burden, we compute the receiver
operating characteristic for the optimized PCA-based cut-off (i.e. 0.99) for both (a)
stand-alone plaque texture-based features and (b) plaque texture-based features
fused with wall-based measurement features, as shown in table 14.13, while the
corresponding visual curves are shown in figure 14.8. Note that we computed
sensitivity, specificity, positive predictive value and AUC for the optimized kernel
only, which is the RBF. As can be seen, the ACU for plaque texture-based fused
with wall-based measurement features was 0.91 compared to 0.86 for the standalone plaque texture-based cRAS system.
14.5.3 Reliability index of the cRAS
In this study, the behavior of the system is analyzed by computing the reliability
index (RI) of the system for both (a) stand-alone plaque texture-based features and
(b) plaque texture-based features fused with wall-based measurement features and is
mathematically given as
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